Arc length
In differential geometry, the arc length of curves is defined, as measure of the total integrated length along a segment of the curve. In a rough sense, it can be imagined as the length the curve would have if it were straightened out into a line.
For a given regular parametric representation f(x) on an interval I of a curve C in the plane, the arc length between points a and b in the interval is equal to the integral:
In general, the arc length formula is a generalization of the distance formula in Euclidean space. It can be defined using a comparable integral, given a metric tensor.
See also
